# Proving 1=2 Bob Ross Style

hi I’m Toby and welcome to another

episode of the joys of mathematics if this is your first time watching then

here’s your chance to go and grab a notepad and pen so you can work along at

home and if you are a returned viewer thanks for coming back now today we’re

going to work through something that’s a little more abstract in its creation and

we’re going to do this to hopefully see that sometimes you can’t always trust

something on its first impression sometimes you need to look a little bit

closer because often things are not as they seem

so keep in mind that this piece today is going to be more of an abstract artwork

than a conventional one so I’ve got my trusty titanium white color here and

let’s get started the first thing that we’re going to do

is we’re going to let a equal b. a and b are our first two characters and they

are variables they could be anything that they ever wanted to be they have

the whole world as their oyster but today a and b have chosen to be exactly

the same thing now as we go along don’t be afraid of the mathematics here I’m

here with you and I’m going to help you go through it well what we’re going to

do is times both sides by b that will give us a times b is equal to b times

itself b squared so we’ve added a couple of happy little b’s here to this line we

added these to both sides so that’s fine we can add or multiply whatever we want

as long as we do it on each side same with division and subtraction there’s a

moral of the story here only do to others what you want done to yourself

and when you’ve got two sides of an equation anything you do to one side you

have to do to the other now let’s add some more happy little b’s and in fact

we’re going to add another b squared to each side of this equation all right got a lot of happy little bs

let’s just simplify this b squared plus b squared

could just be written as 2 b squared and this line for the side says the same now

you might be sort of wondering how this is going to end up anywhere but just

trust me sometimes you need to just go where the wind blows you and it is

pretty windy out here in the garden today I hope that it doesn’t cause too

many issues but let’s just follow along for the drift of the wind here and you

might have to trust me a little bit okay we’ve added b squared what if we do

we’ll got an ab what if we subtract the same term from both sides and that term

is going to be 2ab all right let’s do it to both sides this term that I

subtracted from both sides could have been literally anything since I did it

to both sides and it’s going to make the result the same but up until now we

haven’t done anything illegal with our algebra this is all this is all fine

okay so if we have one ab and we’re taking away 2 ab’s how many ab’s do

we have left well the answer is we’ll still have our b squared and minus one ab and on the side we’ve got to be squared minus 2 ab all right what I

want to do next is to factorize this line and I’m going to continue up here

to do that so there’s one common term to both sides and that is b squared minus ab on this side we could take a 1 out of the bracket if we really wanted to

somewhat unnecessary but we have 1 times B squared minus a B and that is equal to

well we can take a 2 outside the brackets now 2

times b-squared minus a B getting a little close to the edge there but I

think we’re alright okay so now we’ve got this line still nothing illegal has

happened you want to check my algebra you can go through there but now we have

something all right we have B squared minus a B on both sides of the equation

what we may want to do is to recognize that if we divide both sides

by the same thing that’s alright like we can divide both sides by B squared minus

a B and that would be the same as cancelling out this term if we’d

cancelled out this term in brackets then what we have left with is that one is

equal to two now here’s where it appears to be pretty abstract and in fact

something doesn’t quite add up here I’m going to put a little box of shame

around this because this means we’ve done something weird or something

illegal a long way we can’t just suddenly have one being equal to two

because that would fundamentally change so many things about mathematics we rely

on two being exactly double one and not being equal to each other so have a

little look at the algebra and see if you can identify where we went wrong and

why don’t worry if you can’t get it I’m going to show you in just a second but

if you’ve formed your opinion and then let’s have a look I stand by that all of

this algebra is correct the issue comes in at this line here now

we divided both sides by B squared minus a B and that would be fine as long as B

squared minus a B the stuff in brackets was not equal to zero if this stuff was

equal to zero this would amount to dividing both sides by zero and as you

might know dividing by zero is kind of forbidden and mathematics the answer to

that is undefined when you start to viding by zero things in the universe

stop making much sense you could already sort of argue that the

world doesn’t make a lot of sense to us you know good things happen to bad

people all the time and there’s a lot of things that are unexplained but right

here this would give us some weird things dividing by zero leads to all

sorts of things such as that one is equal to two and frankly this is

nonsense so we need to sort this out so let’s have a look B squared since a and

B are equal to each other is actually the same as a times B so this in

brackets is in fact equal to zero and what we have on this line up here is

that one times zero is equal to two times zero now I mean sure anything

times zero is going to be equal to zero so these 1 and two could have been

replaced by literally anything all this really shows is that zero is equal to

zero so if we’ve proved anything that’s what we’ve proved here not that one is

equal to two so there is a bit of a moral here and it was to not trust your

first impressions all the time you know when we did this step it might have

looked like it was legal and this might have looked like a legal result but we

used our sort of critical thinking we realized it probably doesn’t make sense

and there’s probably a reason why so the rule for mathematics is that whenever

you’re going to divide by something check that that something is not zero

but also in life you know sometimes things are too good or too weird to be

true so always look a little closer and don’t just take things at face value now

I’m going to rub this off here and make room for a little message a duster can

get pretty chalky so you just beat the devil out of it this episode of the joys

of mathematics is brough to you Skillshare Skillshare are an online learning

community with classes in things like business design and technology I’m

currently working through some courses on writing short stories and editing

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Skillshare at the link in the description will get two months of

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can find one there that you like this is also your personal invitation to

subscribe to my channel for more videos like this don’t forget to take a closer

look at the world around you and from the bottom of my heart I hope that you

have an absolutely mathematical day here’s some bonus after the credits

footage but I just wanted to show you guys something in the garden it’s over

here and it’s a moth or a butterfly perched on a little branch there now

that’s pretty nice but don’t look too close past him well you might see what

scared me earlier it seems to be a spider I’ll zoom in because I don’t want

to get too close it’s either the spider or like the skin of the spider but to be

honest I didn’t know that spiders head skin so I’m getting out of here

Watch to the end to meet my friends Mr. Spider and Mrs. Butterfly ✨🌿

At 6:47 I intended to say that bad things happen to good people but I guess the other way is also true.

I hav ptsd

"Up until now, we haven´t done anything illegal with our Algebra, this is, this is fine 🙂 "

Proceeds to divide by 0Yawnathon

She use math to destroy math😐🤯

Your existence makes me happy.

Beat the devil out of it. Then you’ll avoid tripping around 1=2.

Is this twooba?

The result is correct because in division you take 1 group and divide it into 2 groups. Like 0 = 1 when referring to how many positions it occupies on the number line.

You are delightful to learn from. Bob Ross would be proud

How can a=b??

Are you High on something

I’m in algebra 1 and I got confused when you removed b from the left side. How did that work? Can you please explain?

Im that one guy that would ask her:

DOyOUlIkE BoB rOsS?what if CAT really spelled DOG???

When I first school I struggled with the fact that five over one equal five. Know that I have taken math through differential equations how can I prove that n/1=n?

….is that a New Zealand Garden ?….

How many numbers is 2?

How wonderful!

If you can let a=a then you can let 1=1 ,if you can let a=b then you can let 1=2 (it's like if you say oranges and bananas tastes the same(not true) you can also say they look the same(not true))

I thought I was good at algebra until this happened.

in a world where a=b, it is possible if you allow 0 to be devided…leaving you with 1=2

in our understanding this cannot be, so you can assume that in our reality a does not equal b.

1 could equal 5 if you'd write: b^2 -ab =5b^2 -5ab

1(b^2 -ab) = 5(b^2 -ab)

1 = 5 🎉

I do not hate math anymore.

Sweetest person on whole tube.

"Let a=b"

Me:

No let 1=2My level of confusion is equal = to ,,,,, (You are Smoking HOT)2 (squared)

Wonderful video..

Yea… she lost me at let a=b.

I don’t see anything happy about this… 🤪🤣

I like you

It is such a joy to learn from you! Thank you!

I actually love these videos

"Note paper and pen" she says…for me it's gotta be note paper and pencil with a BIG eraser. (Love you top, dear.)

Luv u!

Wow!

Squaring is not always doubling.

It s very old stupid ecuation!Every highscool student knows about it!This is a joke!Not math!It 's good when you have a drink with some friends.

This is no more clear than regular math class. VERY confusing.

Still gibberish after all these years. I had to give up going into Mechanical Engineering due to not being able to do the higher forms of math.

If it seems too good to be true…..

Very clever

B squared – ab = 0, and u can't divide by 0

Brilliant

Good teachable moment about math and life. That lovely smile still convinced me that 1=2, though. Which brings us to life lesson #2; a pretty smile can be deceiving, lol.

1:56: Words to live by … Math isn't just a science, it's philosophical too.

ab= a buzzing thing

Did not read other peoples comment. 3:21 is the problem ended up with 0.

Why am I watching this, I hate math.

Let a=b and

Let 1=2

What "universe", Toby? Universe=0 (doesn't exist) and by dividing Truth (Truth=God) by zero, you will always receive zero [i.e. no truth (of God)]. By the way, I just made a=2 & b=2, and found it quite straight forward. God Bless.

I think the spider at the end has had his insides sucked out by another spider.They can inject venom through their bite which liquifies the internal organs and then they are sucked right out!

Hmm i …. hmmm

Hey everybody! don't worry… Division by zero is not illegal!!! You are not going to jail!

I was a math major in college way back in 1990 and I loved math so much I haven't done it in so long and I've just found so much joy in watching your videos thank you

ha ha great bob rosh math lecture series can you do some physics too br style like whats up with f=mxa :P.

Please apply it in the real world. b 2 = 13 what do you mean. Are we building a house or circuit board. It is just b2 =13 ? What do we do now? I need to get rich. Is it going to spit out bitcoin at the end?

Pad and Pen on hand!!!

Well done ❤️

How do you tackle insomnia?

It was two good to be true

2 oranges plus 3 rabbits does not equal 5. Math is only useful at the point is empirically verifiable and terms are defined. mathematical abstraction is deception.

This is peoif that maths is ALL absolute HORSESHIT.

THIS is the way I would want to be parodied: smart, respectful, and funny.

Great videos!!!

Can u explain Ramanujan infinite sum be -12

Found this surprisingly entertaining.

But what if a=0 ?

You can also solve it in another way also

tfw youtube didn't recommend me something that's 7 years old

oI only watch your videos when i feel like wanting something ill never have

i´d tap that, bet shes shy in bed

George Orwell solved almost identical issue in "1984" i.e. 2+2=5; ergo 0=1

p=2×2×2×2×2×2×…=2×p removing the first 2 still produces the same product because infinity-1=infinity

2=p/p=1

Done. Your math test for the day is to explain why my steps were invalid. Have fun.

The problem started with letting a=b. It would be fine if a and b were in separate equations but having them in the same equation renders them superfluous. It's an abuse of the use of variables. Lettering them as different when they are not gives you your problem that you have to figure out at the end and change them back. Otherwise, they are error checked as different and your math has failed.

That's a member of the brush-footed butterfly family and the the spider is either dead or the molted ("skin") exoskeleton of a spider hiding nearby.

You are a goddess

My country isn't making sense – Can I put Trump in a "box of shame"?

Hah, interesting, so it's not only in computer science that you have to always check that you're not dividing by zero.

If you were my math teacher, I would have been good at math.

Finally found Hermione Granger !!

When you transferred the numbers to factorize them you forgot a 2 before the ab near the end of the equation.

That is mathematically very cool, Thanks.

I think there is a simpler discovery that will prevent this paradox; "a" can never be equal to "b" because these 2 language tools have different purposes; "a" is a vowel with many sounds and "b" is a consonant with only 1 sound, so they can never be equal unless you unbend the "a" symbol and reform it as a "b"; straighten the top part to vertical in alignment with the lower part as a vertical line segment and then rotate the entire symbol about the y-axis 180 degrees as that will make a "b". only then can you say b=b. Problem solved.

I think the use of tools from a different paradigm should not be used in the mathematical paradigm and this is why so many people are confused with algebra is because of the use of letters in a numbers world.

Da Fauq

I new it ⚽🎱⚾🏈

At around 10:15 it is not “weird” because she set up 1=2 to begin with. a=1, b=2; therefore, a=b, or 1=2.

daaaaam she is an angel

I met a someone who believed the existence of God will one day be mathematically proved. Can you give that one a try?

Nice! Subscribed. :))

if that's the skin of a spider it probably means there's an even bigger, even badder spider nearby. Good idea to get out of there!!!

2b² or -2b² that is the question

That philosophy is a good philosophy to follow in life. Of never accepting what you first see as the total sum of something, someone or as the correct answer. That first impression rarely tells you the full story. It's like judging a book by its cover, if do not read the book, how can you judge it?

I see it allot with cars. People who rely on the codes. They begin changing components and coming back with the same issue, rather than working the problem to understand the "why" of the problem.

I follow the philosophy in life, of never trusting what you first perceive. Not taking it as the entire truth. Because it may not be..

And btw.. spiders do shed their outer skin's or skeletons as they grow. That appeared to be the outer shell of a huntsman.

Where’s Bob ?

I just leant that there are an infinity of zeros.

a, can never be b, thats an axiom ! nobody can change an axiom !

The confusion is that we cut the (b^2-ab)'s and forget that is just a rude way to say that we're diving the whole equation by (b^2-ab).

Wow …….

you made one of the letters b negative

1 actually equals 3. 😉

Hahahahaha! "good things happen to bad people all the time…" 😀

devided by zero let us free from real number to any complicated number system as the mind want to be. It is interesting that zero is in any frame of reference. It may be a point to visit before go to another frame of reference. Transfomation to some other dimensions. It looks like avantar to any dimension that the soul want to be and get perception. If there are some live form or interested mathematical relations. It may be only the soul part can percept. The mathematics of undefined by real must be created.

Hold the chalk… why exactly does "a" want to = "b" (?) "a" should be content being "a" and not want to = "b" :^)

1=2 = "spooky" action because it's obvious 0 divided by 0 is 1